The forgiving tree: a self-healing distributed data structure

We consider the problem of self-healing in peer-to-peer networks that are under repeated attack by an omniscient adversary. We assume that the following process continues for up to n rounds where n is the total number of nodes initially in the network: the adversary deletesan arbitrary node from the network, then the network responds by quickly adding a small number of new edges.

We present a distributed data structure that ensures two key properties. First, the diameter of the network is never more than O(log Delta) times its original diameter, where Delta is the maximum degree of the network initially. We note that for many peer-to-peer systems, Delta is polylogarithmic, so the diameter increase would be a O(loglog n) multiplicative factor. Second, the degree of any node never increases by more than 3 over its original degree. Our data structure is fully distributed, has O(1) latency per round and requires each node to send and receive O(1) messages per round. The data structure requires an initial setup phase that has latency equal to the diameter of the original network, and requires, with high probability, each node v to send O(log n) messages along every edge incident to v. Our approach is orthogonal and complementary to traditional topology-based approaches to defending against attack.

Development of Disulfiram-Loaded Vaginal Rings for the Localised Treatment of Cervical Cancer

Cervical cancer is the third most prevalent cancer in women and disproportionately affects those in low resource settings due to limited programs for screening and prevention. In the developed world treatment for the disease in the non-metastasised state usually takes the form of surgical intervention and/or radiotherapy. In the developing world such techniques are less widely available. This paper describes the development of an intravaginal ring for the localised delivery of a chemotherapeutic drug to the cervix that has the potential to reduce the need for surgical intervention and will also provide a novel anti-cancer therapy for women in low resource settings. Disulfiram has demonstrated antineoplastic action against prostate, breast and lung cancer. Both PEVA and silicone elastomer were investigated for suitability as materials in the manufacture of DSF eluting intravaginal rings. DSF inhibited the curing process of the silicone elastomer, therefore PEVA was chosen as the material to manufacture the DSF-loaded vaginal rings. The vaginal rings had an excellent content uniformity while the DSF remained stable throughout the manufacturing process. Furthermore, the rings provided diffusion controlled release of DSF at levels well in excess of the IC50 value for the HeLa cervical cancer cell line.

Finite domination and Novikov rings: Laurent polynomial rings in two variables

Let C be a bounded cochain complex of finitely generatedfree modules over the Laurent polynomial ring L = R[x, x−1, y, y−1].The complex C is called R-finitely dominated if it is homotopy equivalentover R to a bounded complex of finitely generated projective Rmodules.Our main result characterises R-finitely dominated complexesin terms of Novikov cohomology: C is R-finitely dominated if andonly if eight complexes derived from C are acyclic; these complexes areC ⊗L R[[x, y]][(xy)−1] and C ⊗L R[x, x−1][[y]][y−1], and their variants obtainedby swapping x and y, and replacing either indeterminate by its inverse.

Evaluation of the Factors Contributing to Levonorgestrel Binding in Addition Cure Silicone Elastomer Vaginal Rings

Background: Following progress of the dapivirine (DPV)-releasing silicone elastomer (SE) vaginal ring (VR) into Phase III clinical studies, there is now interest in developing next-generation rings that additionally provide contraception. Levonorgestrel (LNG) is a safe and effective progestin that is being widely considered for use as a hormonal contraceptive agent in future multipurpose prevention technology (MPT) products. Although LNG has previously been incorporated into various controlled release SE devices, minimal attention has focused on its propensity to irreversibly react with addition cure SE systems. Here, for the first time, we investigate this LNG binding phenomenon and outline strategies for overcoming it.
Methods: VRs containing various loadings of DPV and LNG were manufactured and in vitro release assessed. Different LNG-only SE samples were also prepared to assess the following parameters: (i) addition cure vs. condensation cure SEs; (ii) different types of addition cure SEs; (iii) mixing time, (iv) cure temperature, (v) cure time; and (vi) LNG particle size. After manufacture, the LNG-only samples were assayed for total drug content using a solvent extraction method. The SE curing reaction and the LNG binding reaction was probed using nuclear magnetic resonance (NMR) spectroscopy. Results:
Under certain drug/formulation/processing conditions, LNG was not recoverable from VRs. Further studies using non-ring samples showed that: (a) the phenomenon was only observed with addition cure SEs (and not condensation cure SEs); (b) the extent of binding was dependent upon the type of addition cure SE; (c) micronised LNG showed significantly greater binding than non-micronised LNG; (d) the extent of binding correlated with increased mixing time, cure time and cure temperature.
Conclusions: Careful control of the API characteristics, the SE composition, and the manufacturing conditions will be necessary to establish a practical VR formulation for controlled release of LNG.

Extended Tree Augmented Naive Classifier

This work proposes an extended version of the well-known tree-augmented naive Bayes (TAN) classifier where the structure learning step is performed without requiring features to be connected to the class. Based on a modification of Edmonds’ algorithm, our structure learning procedure explores a superset of the structures that are considered by TAN, yet achieves global optimality of the learning score function in a very efficient way (quadratic in the number of features, the same complexity as learning TANs). A range of experiments show that we obtain models with better accuracy than TAN and comparable to the accuracy of the state-of-the-art classifier averaged one-dependence estimator.

A tree augmented classifier based on Extreme Imprecise Dirichlet Model

We present TANC, a TAN classifier (tree-augmented naive) based on imprecise probabilities. TANC models prior near-ignorance via the Extreme Imprecise Dirichlet Model (EDM). A first contribution of this paper is the experimental comparison between EDM and the global Imprecise Dirichlet Model using the naive credal classifier (NCC), with the aim of showing that EDM is a sensible approximation of the global IDM. TANC is able to deal with missing data in a conservative manner by considering all possible completions (without assuming them to be missing-at-random), but avoiding an exponential increase of the computational time. By experiments on real data sets, we show that TANC is more reliable than the Bayesian TAN and that it provides better performance compared to previous TANs based on imprecise probabilities. Yet, TANC is sometimes outperformed by NCC because the learned TAN structures are too complex; this calls for novel algorithms for learning the TAN structures, better suited for an imprecise probability classifier.

Bayesian network data imputation with application to survival tree analysis

Retrospective clinical datasets are often characterized by a relatively small sample size and many missing data. In this case, a common way for handling the missingness consists in discarding from the analysis patients with missing covariates, further reducing the sample size. Alternatively, if the mechanism that generated the missing allows, incomplete data can be imputed on the basis of the observed data, avoiding the reduction of the sample size and allowing methods to deal with complete data later on. Moreover, methodologies for data imputation might depend on the particular purpose and might achieve better results by considering specific characteristics of the domain. The problem of missing data treatment is studied in the context of survival tree analysis for the estimation of a prognostic patient stratification. Survival tree methods usually address this problem by using surrogate splits, that is, splitting rules that use other variables yielding similar results to the original ones. Instead, our methodology consists in modeling the dependencies among the clinical variables with a Bayesian network, which is then used to perform data imputation, thus allowing the survival tree to be applied on the completed dataset. The Bayesian network is directly learned from the incomplete data using a structural expectation–maximization (EM) procedure in which the maximization step is performed with an exact anytime method, so that the only source of approximation is due to the EM formulation itself. On both simulated and real data, our proposed methodology usually outperformed several existing methods for data imputation and the imputation so obtained improved the stratification estimated by the survival tree (especially with respect to using surrogate splits).

A Tree Augmented Classifier Based on Extreme Imprecise Dirichlet Model

In this paper we present TANC, i.e., a tree-augmented naive credal classifier based on imprecise probabilities; it models prior near-ignorance via the Extreme Imprecise Dirichlet Model (EDM) (Cano et al., 2007) and deals conservatively with missing data in the training set, without assuming them to be missing-at-random. The EDM is an approximation of the global Imprecise Dirichlet Model (IDM), which considerably simplifies the computation of upper and lower probabilities; yet, having been only recently introduced, the quality of the provided approximation needs still to be verified. As first contribution, we extensively compare the output of the naive credal classifier (one of the few cases in which the global IDM can be exactly implemented) when learned with the EDM and the global IDM; the output of the classifier appears to be identical in the vast majority of cases, thus supporting the adoption of the EDM in real classification problems. Then, by experiments we show that TANC is more reliable than the precise TAN (learned with uniform prior), and also that it provides better performance compared to a previous (Zaffalon, 2003) TAN model based on imprecise probabilities. TANC treats missing data by considering all possible completions of the training set, but avoiding an exponential increase of the computational times; eventually, we present some preliminary results with missing data.

NP-hardness of MAP in Ternary Tree Bayesian Networks

This paper strengthens the NP-hardness result for the (partial) maximum a posteriori (MAP) problem in Bayesian networks with topology of trees (every variable has at most one parent) and variable cardinality at most three. MAP is the problem of querying the most probable state configuration of some (not necessarily all) of the network variables given evidence. It is demonstrated that the problem remains hard even in such simplistic networks.

Finite domination and Novikov rings. Laurent polynomial rings in several variables

We present a homological characterisation of those chain complexes of modules over a Laurent polynomial ring in several indeterminates which are finitely dominated over the ground ring (that is, are a retract up to homotopy of a bounded complex of finitely generated free modules). The main tools, which we develop in the paper, are a non-standard totalisation construction for multi-complexes based on truncated products, and a high-dimensional mapping torus construction employing a theory of cubical diagrams that commute up to specified coherent homotopies.